Have the “wah-wah” sound produced by two musical instruments that are slightly out of tune ever occurred to we? Beats are the term for the fading effect. The meeting of two sounds with slightly differing frequencies is a cool phenomena.
What Are Beats?
Interference occurs when two sound waves with almost identical frequencies move with racing bike. Constructive interference occurs when their peaks and valleys coincide, amplifying the sound. The sound becomes weaker when they occasionally cancel each other out (destructive interference). We perceive these regular increases and decreases in volume as beats.
Beats Frequency Formula and Important Point
The phenomenon of regular variation in intensity of sound with time at a particular position due to superposition of two sound waves of slightly different frequencies is called beats.
For waves
y1 = a sin ω1t = a sin 2πv1 t
y2 = a sin ω2t = a sin 2πv2 t
Therefore, y = 2a cos π (v1 – v2)t. sin π(v1 + v2)t is the required equation of beats.
Beat frequency vbeat = v1 – v2
Beat period, T = 1 / beat frequency = 1 / v1 – v2
Superposition of two harmonic waves, one of frequency 15 Hz and the other of frequency 13 Hz, its give rise to beats of frequency 2 Hz.
Beats are just the rhythmic “pulses” or “fluctuations” in the intensity of sound.
How Do Beats Happen?
Suppose a pair of tuning forks. At 256 Hz, one vibrates, and at 260 Hz, the other. We do not hear a single, continuous sound when we strike both at once. Instead, we hear the sound constantly becoming louder and softer. This occurs as a result of:
The sound is loud when the sound waves are precisely aligned;
The sound is muted when they are out of step; and
This cycle repeats at regular intervals.
The beat frequency is the number of times the loudness rises and falls in a single second.
Formula for Beat Frequency
The beat frequency (f beats) is simply the difference between the frequencies of the two sources:
fbeats = ∣f1−f2∣
where:
f1 is the frequency of the first wave,
f2 is the frequency of the second wave,
∣∣ means we take the absolute (positive) value
Example:
If two tuning forks have frequencies 300 Hz and 305 Hz,
fbeats = ∣300−305∣ = 5 beats per second means we will hear 5 beats every second.
Important Points About Beats
Condition: Beats are only audible when there is a tiny frequency difference between the two (usually less than 10 Hz). We will not hear beats if the difference is too great; instead, we will hear two distinct noises.
Amplitude: Due to alternating constructive and destructive interference, the volume of sound varies during beats.
Same Medium: The two sound waves must pass through the same medium (such as air) in order for beats to develop correctly.
Applications:
Musicians use beats to tune instruments accurately.
In science, beats help in measuring unknown frequencies.
Visualising Beats
The frequency of one wave is a little higher. When we combine these two waves, we will see a pattern where the height of the waves frequently rises and falls; this is how beats seem visually.
Even a fun experiment can be tried at home. Play two noises on two different mobile phones (there are a lot of apps for this), and pay close attention to what each one sounds like. The beat effect will be audible to we.
Mathematical Derivation (for those curious)
If two waves are:
y1 = A sin(2πf1t)
y2 = A sin(2πf2t)
Their combination becomes:
y = 2 A cos(2π f1−f2 / 2 t) sin(2πf1 + f2 / 2 t)
Here:
The term cos(2πf1 − f2 / 2 t) controls the amplitude.
It oscillates with frequency ∣f1−f2∣, so the sound fluctuates accordingly.
Note:
Phenomenon of beats can be used to determine the frequency of tuning fork as follows:
If vA is known frequency of tuning fork A and vB is unknown frequency of tuning fork B. When both tuning forks A and B are sounded together, and produced beats of frequency v, then vg = vA +- v. Here, the +- sign of v is decided either by loading wax or by filing any one of the tuning forks.
If the tuning fork B is loaded with wax, and sounded with the tuning fork A, if the beat frequency increases, then vB = vA – v. If beat frequency decreases, then vB = vA + v.
If tuning fork B is field and sounded with the tuning fork A, if the beat frequency increases, then vB = vA + v. If the beat frequency decreases, then vB = vA – v.
Conclusion
Beats are the beautiful outcome of two nearby frequencies dancing together. The phenomena benefits both scientists and musicians since it is the ideal fusion of art and physics. Keep in mind that we are experiencing the attraction of beats every time we hear the “wah-wah” sound produced by two adjacent tones.
Beats occur when two sound waves with slightly differing frequencies interfere with one another, causing periodic changes in sound intensity. A “beat” impression is produced when these waves combine to produce a sound that alternates between loud and faint.
The beat frequency is calculated using the formula:
fbeats = ∣f1 − f2∣
Where f1 and f2 are the frequencies of the two sound sources. The result is the number of beats heard per second.
The beats are sluggish and audible if there is little (less than 10 Hz) difference between the two frequencies. The beat effect vanishes if the difference is significant because our ears perceive two distinct sounds rather than a single oscillating sound.
Tuning musical instruments: To match frequencies, musicians tune their instruments by listening for beats and decreasing them.
Measuring unknown frequencies: To precisely ascertain the frequency of an unidentified sound source, scientists employ beats.